Numerical simulating wave propagation over solid obstructions using a non-hydrostatic free surface flow model combined immersed boundary method

Abstract

The vertical transformed σ-coordinate adopted by a family of non-hydrostatic free surface water flow models is highly efficient in capturing the free surface and uneven bottom. Nevertheless, it is difficult to simulate flows around complex solid obstructions. In this paper, the immersed boundary method (IBM) is developed and implemented in a non-hydrostatic wave model to promote the ability in simulating wave interactions with solid structures. In the IBM spirit, a virtual force term is introduced into the momentum equations to mimic the natural physical boundary conditions. The virtual force terms are added on the named ghost cells neighboring the solid boundary to enforce the no-slip velocity condition on the solid wall. An efficient and robust method is promoted to identify the virtual solid boundary and the ghost cells. A set of test cases are implemented to verify and validate the proposed model in modeling water wave interaction with solid obstructions. The free surface flow model coupled with IBM is well verified, accurate and efficient in modeling wave-structure interaction and is expected to promote the model in engineering applications.